Emilia Petrisor
Nontwist area preserving maps with reversing symmetry group
(66K, LATeX 2e)
ABSTRACT. The aim of this paper is to give a theoretical explanation of the
rich phenomenology exhibited by nontwist mappings of the cylinder,
in numerical experiments reported in {[del-Castillo {\it et al},
1996]}, {[Howard \& Humpherys, 1995]},
and to give new insights in the dynamics of nontwist
standard--like maps. Our approach is based on the reversing
symmetric properties of the nontwist standard--like systems. We
relate the bifurcation of periodic orbits of such maps to their
position with respect to a group--invariant circle, and to a
critical circle, at whose points the twist property is violated.
Moreover, we show that appearance of the meanders, i.e.
homotopically nontrivial invariant circles of the cylinder,
that are not graphs of real functions of angular variable,
is a global bifurcation of a curve on the cylinder,
with nodal--type singularities, and invariant with respect to the
action of a reversing symmetry group.